Ex 3.2 Q3 (ii) - The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Ex 3.2 Q3 (ii) - The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Ex 3.2 Q3 (ii) - The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.

Solution:-

Let,
      Larger angle = x
      Smaller angle = y

Case (i): The larger angle exceeds the smaller angle by 18 degrees,

   ∴ x = y + 18°       ------- (i)

Case (ii): We know that, the sum of the measures of angles of a supplementary pair is always 180°,

   ∴ Sum of both angles = 180°
   ∴ x + y = 180°
   ∴ y + 18° + y = 180°       { from (i) }
   ∴ y + y = 180° - 18°
   ∴ 2y = 162°
   ∴ y =
162° / 2
   ∴ y = 81°

➙ Putting y = 81° in Eqⁿ(i)

   ∴ x = 81° + 18°
   ∴ x = 99°

Therefore,
      Larger angle = x = 99°
      Smaller angle = y = 81°

Hence,
          The larger and smaller angles are 99° and 81° respectively.
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Try This..

✒ Find two supplementary angles such that one is twice the other.

✒ One angle is 20° less than its supplement. What are the angles?

✒ Two angles are supplementary. If one angle is three times the other, find them.

✒ The difference between two supplementary angles is 30°. Find the angles.

❌ Common Mistakes

Forgetting the sum of supplementary angles is always 180°:
▸ Always remember; supplementary angles add up to 180°, not 90° (that’s complementary!).

Wrong variable assignments:
▸ Clearly define what each variable stands for; smaller vs. larger angle.

Algebraic errors while solving:
▸ Keep your algebra steps clean and double-check calculations.

Skipping the verification step:
▸ Always add the final angles to see if they make 180°. This builds confidence and avoids careless mistakes.

📝 Related Questions:-


Queries Solved:-

Class 10 Ex 3.2
Ex 3.2 Q3 ii Class 10
Class 10 Ex 3.2 Q3 ii
Class 10 Chap 3 Ex 3.2 Q3 ii
Class 10 Pair Of Linear Equations in Two Variables

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